Which pair of equations generates graphs with the same vertex?

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Which pair of equations generates graphs with the same vertex?A) y = –(x + 4)2 and y = (x – 4)2
B) y = –4×2 and y = 4×2
C) y = –x2 – 4 and y = x2 + 4
D) y = (x – 4)2 and y = x2 + 4


A quadratic equation may be expressed in vertex form as:
y = a(x – h)² + k, the vertex being (-h , k)
For option A, the vertices are visibly different. (-4 , 0) and (4 , 0)
For B, the graphs’ vertices are the same, (0 , 0).
For C, the vertices (can be obtained by differentiating and putting equal to 0) are (0 , -4) and (0 , 4)
For D, the vertices are (4 , 0) and (0 , 4)
Thus, the answer is B.

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